Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary mass, stiffness and damping

Abstract In this paper, the flutter instability characteristics and mechanisms of the weakly damped Ziegler double pendulum subjected to the follower type circular loading are investigated. The double pendulum is assumed to be with arbitrary masse, stiffness and damping. Different with the existed mathematical analysis methods, the pendulum flutter instability conditions and the corresponding critical parameters are theoretically deduced and evaluated based on an energy method with clear physical meanings. By introducing the ratio parameters of the structural mass, stiffness and damping coefficients, the complex influences of the structural mass, stiffness and damping are discussed in details. In addition to the counter-intuitive “damping Ziegler Paradox” influence, the stabilizing and destabilizing influences of the pendulum’s mass and stiffness are observed and investigated. To clarify these complex influences, the power flow characteristics on the pendulum flutter instability occurrence are investigated. The results indicate that the mass or stiffness related powers on each coordinate constitute the two “power exchange twins”, and can affect the related destabilizing or stabilizing influences of the pendulum mass and stiffness, while the “damping Ziegler Paradox” influence can be affected by the energy transmission efficiency between the stiffness related powers on each coordinate. Correspondingly the flutter instability physical mechanisms are clarified for the first time from the energy perspectives.